Question

motor boat whose speed is 24 km/hr in still water takes 1 hr more to go 32km upstream than to return downstream to the same spot. Find the speed of the stream.

Answer 1

the speed of stream be x.

Then,

Speed of boat in upstream is 24 ‒ x

In downstream, speed of boat is 24 + x

According to question,

Time taken in the upstream journey ‒ Time taken in the downstream journey = 1 hour

Answer 2

Answer:

Let the speed of stream be x.

Then,

Speed of boat in upstream is 24 ‒ x

In downstream, speed of boat is 24 + x

According to question,

Time taken in the upstream journey ‒ Time taken in the downstream journey = 1 hour

$\implies\tt \dfrac{32}{24 - x} - \dfrac{32}{24 + x} = 1 \\\\\\\implies\tt\dfrac{24 + x - 24 + x}{{24}^{2} -{x}^{2}} = \dfrac{1}{32} \\\\\\\implies\tt \dfrac{2x}{576 -{x}^{2}} = \dfrac{1}{32}\\\\\\\implies\tt 2x \times 32 = 576 -{x}^{2}\\\\\\\implies\tt {x}^{2} + 64x - 576 = 0\\\\\\\implies\tt {x}^{2} + 72x - 8x - 576 = 0\\\\\\\implies\tt x(x + 72) - 8(x + 72) = 0\\\\\\\implies\tt (x - 8)(x + 72) = 0\\\\\\\implies\tt \green{x = 8} \quad or \quad \red{x =- 72}$

⠀

∴ Speed of the Stream will be 8 km/hr.